Understanding of Extreme Events: Hansen, Sato, and Ruedy

James Hansen and colleagues (HSR) have a new manuscript posted that’s been receiving some attention. It hasn’t been submitted anywhere yet, nor has it been decided whether they’ll turn it into a manuscript for submission. Like the paper by Rahmstorf and Coumou, it considers how the odds of extreme events have changed, with a focus on summer temperatures. Unlike Rahmstorf and Coumou, it considers extreme events that exceed a certain threshold, rather than extreme events that set a record.

The threshold is defined as a particular number of standard deviations (conventionally represented with the greek letter “sigma”) beyond the 1951-1980 mean. The choice of 1951-1980 is natural, since it’s the baseline period for Hansen’s GISS global temperature analyses. Still, it bears remembering in what follows that when they talk about a “3-sigma” event, they’re talking about three standard deviations above the 1951-1980 mean, not three standard deviations above the period of record mean. And their standard deviation is calculated based on a detrended 30-year period, so as to ensure that only the high-frequency variability contributes to the standard deviation. Inevitably, it’s generally smaller than the standard deviation that would be calculated from a longer not-detrended period of record.

So HSR’s “3-sigma” event is not what you or I would normally call a “3-sigma” event. Strictly speaking, it’s what a 3-sigma event would be if the climate were stationary about the 1951-1980 period. Henceforth, I’ll call such an event a mid-century 3-sigma event. This is just a terminology issue, but one that can lead to misinterpretation when the paper is summarized.

HSR show that mid-century extreme high temperature events (0.43 sigma, 2 sigma, and 3 sigma) have become much more common as a percentage of surface area across the Earth. The rarer the event, the bigger the effect; in the past three years, mid-century 3-sigma anomalies have affected 6%-13% of the Earth’s surface, compared to an expectation of 0.1%-0.2% in an unchanging climate. The Russian heat wave of 2010 and the Texas heat wave of 2011 were both mid-century 3-sigma events.

(Note that the 0.1%-0.2% assumes that the probability distribution is Gaussian; non-Gaussian distributions could raise or lower that number. Also, it assumes that the mean and standard deviation are estimated perfectly from a mere 30 years of data; random errors in estimation will lead to an overall increase in out-of-sample three-sigma events. The true expectation is calculable; somebody ought to go ahead and calculate it.)

HSR look at how the distribution has changed over time. Scaled locally by standard deviation, the distribution of events has shifted toward the warm side, producing a large increase in the frequency of events in the 2-sigma and 3-sigma categories. HSR also note that the distribution of temperatures has broadened, but they note that the temperature distribution in their analysis mid-century was artificially narrow because of a lack of data in the Southern Ocean, so it’s not clear to me how much of the broadening is real and how much is artificial.

Some interesting issues arise when HSR conclude that “One implication of this shift is that the extreme anomalies in Texas in 2011, in Moscow in 2010, and in France in 2003 almost certainly would not have occurred in the absence of the global warming with its resulting shift in the distribution of anomalies. In other words, we can say with a high degree of confidence that these extreme anomalies were a result of the global warming.” Later on, the discuss blaming the Texas heat wave on La Nina and end up qualifying the statement somewhat: “Today’s extreme anomalies occur because of simultaneous contributions of specific weather patterns and global warming.”

I think that in the end, HSR get it right: the 2011 Texas heat wave occurred because of simultaneous contributions of specific weather patterns and global warming, with other minor contributions from other factors. Their statements elsewhere in the paper that the extreme anomalies were a result of the global warming, period, are too much of a stretch.

The abstract of the paper phrases things a bit differently: “Thus there is no need to equivocate about the summer heat waves in Texas in 2011 and Moscow in 2010, which exceeded 3-sigma – it is nearly certain that they would not have occurred in the absence of global warming.” This statement, like similar statements by Rahmstorf and Coumou, is fine in the absence of knowledge about the specific event, but we actually know a lot about the specific events. So I’ll dig a bit deeper into the Texas 2011 event.

The average Texas temperature in June-August 2011, according to the latest numbers from the National Climatic Data Center, was 86.7F. The average for the period 1951-1980 was 81.3F. The detrended standard deviation for the period 1981-2010 was 1.07F. So the anomaly relative to 1951-1980, 5.4F, was 5.0 standard deviations above the 1951-1980 mean.

HRR say that the choice of period for estimating the standard deviation doesn’t matter much, but in some places (such as this one), it does matter. The standard deviation for the period 1951-1980 was 1.53F, so by that measure the 5.4F anomaly was “only” 3.5 standard deviations above the 1951-1980 mean.

How much of that was due to climate warming? I attributed 0.9F of the excess Texas heat (compared to 20th century averages) to climate warming in my earlier back-of-the-envelope attribution. The 20th century average and 1951-1980 average are about the same in Texas, so the same number works here. Without climate warming, the anomaly relative to 1951-1980 would have been only 4.5F, which is only 2.9 to 4.2 standard deviations above the 1951-1980 mean. So, if my attribution analysis is correct, it still seems likely that the 2011 Texas heat would have exceeded HSR’s three-sigma value without climate warming.

But at this point we’re talking arbitrary thresholds. According to my attribution analysis, and defining the mean and standard deviation the normal way using the period 1895-2010, 2011 was a 4.2-sigma event, and it would not have been a 4-sigma event without climate warming.

Note that this is different from saying that the 2011 Texas heat would not have occurred at all without the climate warming, which HSR could be wrongly interpreted as saying.

Taking the frameworks of the Rahmstorf-Coumou and Hansen-Sato-Ruedy papers together, it is plain that heat records should and are increasing, and hot episodes should and are becoming more extreme, as the climate warms. In the specific case of the Texas 2011 heat, natural factors appear to have been so strong that it would have set a record even in the absence of climate warming, but it would almost certainly not have been so intense as to be four sigmas above the long-term average without the contribution of climate warming.

In other words, nature made it a record. Climate change made it a phenomenal record.

9 Responses

I certainly hope nobody is claiming that “the 2011 Texas heat would not have occurred at all without the climate warming”. That is certainly not my interpretation.

As Meehl alluded to recently, we have climate on steroids thanks to higher levels of GHGs. What are your thoughts on the magnitude of the impacts of ENSO in a warming world? Ignoring for now any possible changes in their intensity or frequency.

[Al – Good question. There must be a couple of studies on this; I’ll have to poke around unless someone else out there can point me in the right direction. – John N-G]

Both the Cook, Stahle, et al. (2004) and Seager et al. (2007) papers on the increasing aridity trend in the southwest discuss some of the implications of ENSO on a base climate that is warmer. Here is the last sentence from the Seager article:

“The most severe future droughts will still occur during persistent La Niña events, but they will be worse than any since the Medieval period, because the La Niña conditions will be perturbing a base state that is drier than any state experienced recently.”

As someone who actually took a class on this sort of stuff back in grad school I believe that the main issue with “Global Warming” is how badly the “Experts” have explained it to the general population. First off, calling it “Global Warming” is a misnomer, “Climate Change” is much more appropriate and accurate. Also we are not talking about a completely “man-made” phenomena, rather we are discussing what in the data I have seen is ~ 30% above “natural” variation levels in subject gasses.
Is the climate changing? YES… Get over it, get used to it, and we as an intelligent species (well, except for the majority of the GOP Presidential hopefuls)need to use said intelligence to ADAPT to the now changing conditions, be they stronger and more frequent storms or record breaking heat and drought…

Your mathematical analysis was informative, accurate, mathematical and boring. The HSR paper, on the other hand, has pretty pictures, lots of color, an excellent straw man argument (Texas is hot, therefore, global warming is caused by CO2 emissions) and even a non sequitur political statement. How can you hope to compete with such showmanship? You’re really going to have to spice it up if science is going to have a chance.

As to Hansen’s latest political paper dressed up as science?
Why do many consider Hansen and pals experts on species extinction, botany, energy markets, politics, regional weather issues, etc. when he is none of those?

hunter. Being a scientist himself, Hansen is quite comfortable referring to and relying on the expertise of other scientists in fields that he’s not personally investigated. He does have enough expertise to review literature and ask questions of relevant people. You might also bear in mind that he’s a bit of a workaholic. I wouldn’t be surprised if it turned out that he had acquired direct, personal expertise in some of these areas.

“Is what is shown here still “how science is done”?”

In my experience it’s certainly how philosophy and a couple of other disciplines are done. Challenging, persistent and argumentative, moving briskly along to impolite, abrasive, sometimes downright rude. Academics seem to save supportive and helpful attitudes for their students, sometimes not even then. (Though they’re just like anyone else when it comes to personal matters like illness in the family.)

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[Editor’s note: I deal with lots of spam (presently about 30 entries per day) that purport to compliment my blog while simultaneously embedding links to bootleg merchandise outlets. This example is merely the most incoherent of them. – John N-G]